Abstract
In this paper, we deal with new equivalent conditions for the localized weak Radon-Nikod\'ym property in dual Banach space related to set-valued operators. First, we introduce the geometric definition of the weak Radon-Nikod\'ym property and the weakly fragmented set-valued operator. Next, using the weakly fragmented mapping, we reveal the relation between the weak Radon-Nikod\'ym property and the weakly single-valued operator. Finally, using this relation and the concept of the exposed point, the main theorem is given together with some applications.
Citation
Keun Young Lee. "New criteria for the weak Radon-Nikodým property related to set-valued operators." Rocky Mountain J. Math. 45 (5) 1511 - 1526, 2015. https://doi.org/10.1216/RMJ-2015-45-5-1511
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